Question

olivia is choosing a pair of socks and a pair of shoes. for the socks, she can choose from red and blue and for the shoes, she can choose from sandals, loafers, sneakers, and boots. what is the sample space of one pair of socks and one pair of shoes?
how many possible outcomes are there?

	sandals	loafers	sneakers	boots
red	red, sandals	red, loafers	red, sneakers	red, boots
blue	blue, sandals	blue, loafers	blue, sneakers	blue, boots

there are \\(\square\\) outcomes.

Explanation:

Step1: Identify number of sock choices

There are 2 choices for socks (red, blue).

Step2: Identify number of shoe choices

There are 4 choices for shoes (sandals, loafers, sneakers, boots).

Step3: Calculate total outcomes

Use the multiplication principle: total outcomes = number of sock choices × number of shoe choices = \(2\times4 = 8\).
Or count from the table: 4 outcomes for red socks + 4 outcomes for blue socks = 8.

Answer:

8